Summary: The Dependency Pair Framework: Combining
Techniques for Automated Termination Proofs #
J˜urgen Giesl, Ren’e Thiemann, Peter Schneider­Kamp
LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany
{giesl|thiemann|psk}@informatik.rwth­aachen.de
Abstract. The dependency pair approach is one of the most powerful
techniques for automated termination proofs of term rewrite systems. Up
to now, it was regarded as one of several possible methods to prove ter­
mination. In this paper, we show that dependency pairs can instead be
used as a general concept to integrate arbitrary techniques for termina­
tion analysis. In this way, the benefits of di#erent techniques can be
combined and their modularity and power are increased significantly. We
refer to this new concept as the ``dependency pair framework '' to distin­
guish it from the old ``dependency pair approach ''. Moreover, this frame­
work facilitates the development of new methods for termination analy­
sis. To demonstrate this, we present several new techniques within the
dependency pair framework which simplify termination problems consid­
erably. We implemented the dependency pair framework in our termina­
tion prover AProVE and evaluated it on large collections of examples.
1 Introduction